Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 902506, 30 pages
doi:10.1155/2009/902506
Research Article
Quantum Energy Expectation in Periodic Time-Dependent Hamiltonians via Green Functions
1Departamento de Matemática, Universidade Federal de São Carlos, 13560-970 São Carlos, SP, Brazil
2Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada
3Instituto de Ciências Exatas, Universidade Federal de Itajubá, 37500-000 Itajubá, MG, Brazil
Received 10 November 2008; Revised 29 January 2009; Accepted 21 February 2009
Academic Editor: Edson Denis Leonel
Copyright © 2009 César R. de Oliveira and Mariza S. Simsen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let UF be the Floquet operator of a time periodic
Hamiltonian H(t).
For each positive and discrete observable A (which we call a probe energy), we derive a formula for the Laplace time average
of its expectation value up to time T in terms of its eigenvalues and Green functions at the circle of radius e1/T. Some simple applications are provided which support its usefulness.